Exploring Tetrachordal Voice-Leading Spaces Within and Around the MORRIS Constellation

Mark Sallmen

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Musicology and Musical Analysis Music Technology and Sound Studies Literature, Musicology, and Cultural Analysis

Abstract

1] Building on Robert Morris's (1990) research on hexachordal ZC-relations, Stephen Soderberg (1998) identifies a constellation of ten hexachords that embed either one diminished seventh chord or two diminished triads.Soderberg divides the constellation, called MORRIS (or T-HEX), into four overlapping eight-hexachord sub-constellations based on tetrachordal subset content.The first of these sub-constellations, TRISTAN, includes the hexachords that embed two instances of set class 4-27[0258], the set class of the major-minor and half-diminished seventh chords.Similarly, constellations ZAUBER, AGITATION, and BROODING include the hexachords that embed two instances of set classes 4-18[0147], 4-13[0136], and 4-12[0236], respectively.Soderberg characterizes each of these tetrachordal set types as a "warp" of the diminished seventh chord.When the "warp index," w, is 1, the result is set class 4-27-that is, moving any pc of a diminished seventh chord by interval class (ic) 1 creates a member of set class 4-27.Similarly, setting w = 2, 4, and 5 creates set classes 4-18, 4-13, and 4-12, respectively.The article goes on to point out a general property of voice leading: in each hexachord the pair of tetrachords can be connected by holding two pitch classes in common and by moving two others by ±w.The cases involving 4-27 and ic 1 voice leading (TRISTAN) are familiar-ii -V 7 , the Tristan chord with resolution, A 7 -B 7 at the beginning of Debussy's Faune, and others-and have been addressed in the theoretic literature by several authors.(1) Example 1 presents the MORRIS constellation and its four overlapping sub-constellations, henceforth called Volume 17, Number 4, December 2011

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References

1996Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late-Romantic Triadic Progressions 1997Neo-Riemannian Operations, Parsimonious Trichords, and Their "Tonnetz" Representations 1998Parsimonious Graphs: A Study in Parsimony, Contextual Transformations, and Modes of Limited Transposition 2008Generalized Voice-Leading Spaces 1987Composition With Pitch-Classes 1995Reimag(in)ing Riemann 1998Some Aspects of Three-Dimensional "Tonnetze"2003Uniformity, Balance, and Smoothness in Atonal Voice Leading

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